This article describes a way to assemble the cheiroballistra arm. Another perfectly valid method is described in the Attaching the bar to the cone article; the other method is somewhat more durable, because the bar runs down the entire length of the cone. More theoretical details on the arms are available at the Cheiroballistra arms article.
The process step-by-step Edit
Measure the correct distance from the end of the cone and file a shallow grooves for the hoop to opposing sides of the cone:
These shallow, round grooves on the sides help prevent the hoop from moving during pullback. They are also (relatively) safe, because the cone is rounded quite heavily, and only the the topmost part at the back and the belly are stressed to any reasonable extent during pullback. In other words, the sides of the cone are - with grooves or no grooves - basically just dead mass that stabilizes the arms.
Note that you must not file a groove to the top nor the bottom of the cone, or you will weaken the arms considerably, by cutting through wood fibers which either bend (at the back) or compress (at the belly) a great deal during pullback.
Once grooves have been filed (if not earlier), push the bar down the groove until the hook rests against the thin part of the cone. Then lightly squeeze the hoops to the groove so that the open end is placed to the side:
Once the alignment of the hoop is correct, squeeze it tight. Then attach the bar to a vise and bend the end of the bar tightly around the hoop with a hammer, pliers, the vise or whatever:
Finally cut the end of the bar and squeeze the remainder against the hoop: